Due to a plethora of algorithmic and theoretical applications, significant amounts of research effort are spent on introducing and studying new sorts of decompositions (along with corresponding width measures) that capture specific classes of objects and/or structural correspondences. These include e.g. modular decompositions [1]}, partitive families [2]}, [3]}, clique-width decomposition trees [4]}, [5]}, branch decompositions [6]} and rank decompositions [7]}.
